Signal-to-Noise-Ratio Improvement in a PCM System

It is shown for a PCM system that the output signal-to-noise power ratio expressed in decibels is approximately equal to twice the input signal-to-noise power ratio. It is independent of the number of code pulses when a sufficient number are used. The dis-tortion due to quantization varies greatly with the number of levels. Adopting the criterion that the output noise power should equal the distortion power, a relation giving corresponding values of the number of digits and input signal-to-noise ratio is found.